Neural Networks and the Chomsky Hierarchy — part 6/6

Cleaned-text code points [76804, 78408). Bibliography omitted here; source.md includes it.

To provide a more detailed empirical result, we train the transformer encoder with relative positional encodings for increasing numbers of in-distribution data points ( 100 000 100\,000 , 1 000 000 1\,000\,000 , and 10 000 000 10\,000\,000 training steps) and increasing numbers of layers (5, 10, 15, 20, 25). Table B.6 shows that the score, i.e., the accuracy averaged over all (unseen) test lengths and maximized over 10 seeds and 3 learning rates, generally does not increase with more training data or more parameters. Thus, in this empirical setup, the Chomsky hierarchy implies a hard limit on scaling laws ( Kaplan et al., 2020 ) .

## Instructions for reporting errors

We are continuing to improve HTML versions of papers, and your feedback helps enhance accessibility and mobile support. To report errors in the HTML that will help us improve conversion and rendering, choose any of the methods listed below:

Click the "Report Issue" ( ) button, located in the page header.

Tip: You can select the relevant text first, to include it in your report.

Our team has already identified the following issues . We appreciate your time reviewing and reporting rendering errors we may not have found yet. Your efforts will help us improve the HTML versions for all readers, because disability should not be a barrier to accessing research. Thank you for your continued support in championing open access for all.

Have a free development cycle? Help support accessibility at arXiv! Our collaborators at LaTeXML maintain a list of packages that need conversion , and welcome developer contributions .